By Xavier Leroy (auth.), Franz Baader (eds.)

The 18th foreign convention on Rewriting innovations and functions, held in Paris, France in June 2007, featured shows and discussions centering on many of the most up-to-date advances within the box. This quantity provides the lawsuits from that meeting.

Twenty-four revised complete papers are offered, in addition to 3 platforms description papers and 3 invited talks. all of the papers was once subjected to a cautious overview procedure. The editor has ensured that all of them meet the top criteria of analysis and scholarship.

Papers hide present learn on all points of rewriting, together with functions, foundational matters, frameworks, implementations, and semantics. this is often advised examining for someone who desires to examine extra approximately a few of the most up-to-date advances in rewriting concepts and applications.

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Extra resources for Term Rewriting and Applications: 18th International Conference, RTA 2007, Paris, France, June 26-28, 2007. Proceedings

Example text

A public function symbol is R0 -resistant iff it is not R0 -transparent. Private functions will be considered to be resistant, for any intruder system R0 . By definition, an R0 -resistant term is one whose top-symbol is R0 -resistant. Let R be any convergent intruder TRS, and a simplification ordering containing R. ) We assume that satisfies the block-ordering property: every private symbol is higher than every public symbol under . We shall denote by Δ a subsystem consisting of (some of the) dwindling rules in R.

If the number of variables that occur more than once in the lhs of the rules in R is fixed, we get a polynomial-time algorithm by Proposition 8; and this gives: Proposition 10. Let k be a fixed natural integer, and R a dwindling TRS such that, for each l → r ∈ R the number of variables in V ar(l) V ar(r) that occur more than once in l is less than k. Then, the general cap problem over R, and a given set of private terms S, is decidable in polynomial time over ||R|| and |S|. 8 Δ-Strong Intruder Theories Let R0 be any given convergent intruder TRS.

We then have: Lemma 6. The saturation of any given set of private terms S can be done in NTIME(φ(|S|, ||R||)), where φ is a polynomial with two arguments. Proof. Every term added under an inference is a proper subterm of some term in S; by Proposition 7 each inference step can be performed in NP time. If the number of variables that occur more than once in the lhs of the rules in R is fixed, we get a polynomial-time algorithm by Proposition 8; and this gives: Proposition 10. Let k be a fixed natural integer, and R a dwindling TRS such that, for each l → r ∈ R the number of variables in V ar(l) V ar(r) that occur more than once in l is less than k.

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